An entanglement measure for n qubits

Li, Dafa; Li, Xiangrong; Huang, Hongtao; Li, Xinxin

doi:10.1063/1.3050298

Cited by 21 publications

(26 citation statements)

References 20 publications

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“…An example of a nonlinear 1-E function, satisfying (4), is E (N ) (e 1 ) = λ 1−N (e 1 ) N , λ ∈ R + . Indeed for λ = 1 this describes a multiplicative measure E (N ) (e 1 ) = (e 1 ) N as in the case of the pure-state entanglement measure defined in [17,18] for N even. We will have more to say about the solutions of (4) later.…”

Section: Scalabilitymentioning

confidence: 99%

Characterizing scalable measures of quantum resources

Parisio

2019

Preprint

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The question of how quantum resources, like entanglement and coherence, depend on the number of copies is addressed. We define scalable quantities E (ρ ⊗N ) as physically consistent measures that can be described as functions of the variables {E (ρ ⊗i 1 ), E (ρ ⊗i 2 ), . . . , E (ρ ⊗iq ); N } for N > ij . If analyticity around vanishing resources is assumed, recursive relations can be derived for the Maclaurin series of E (ρ ⊗N ), which enable us to determine the possible functional forms. In particular, we find that if E (ρ ⊗2 n ) depends only on E (ρ), E (ρ ⊗2 ), and n, then it is completely determined by Fibonacci polynomials, to leading order. We show that the one-shot distillable (OSD) entanglement is well described as a scalable measure for several families of states. For a particular two-qutrit state ̺, we determine the OSD entanglement for ̺ ⊗96 from smaller tensorings, to leading order, with an accuracy of 97% and no extra computational effort.

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Section: Scalabilitymentioning

confidence: 99%

Characterizing scalable measures of quantum resources

Parisio

2019

Preprint

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“…(1.7) is considered as the residual entanglement for odd n qubits in [23] and [26]. From the above discussion, we can say that for odd n qubits, |GHZ possess the maximal residual entanglement τ = 1 while the residual entanglement τ for the Dicke states |l, n vanishes.…”

Section: All the N-qubit Symmetric Dicke States Are Inequivalent To Tmentioning

confidence: 99%

Stochastic local operations and classical communication properties of the n-qubit symmetric Dicke states

Huang

et al. 2009

Europhys. Lett.

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Recently, several schemes for the experimental creation of Dicke states were described. In this paper, we show that all the n-qubit symmetric Dicke states with l (2 ≤ l ≤ (n − 2)) excitations are inequivalent to the |GHZ state or the |W state under SLOCC, that the even n-qubit symmetric Dicke state with n/2 excitations is inequivalent to any even n-qubit symmetric Dicke state with l = n/2 excitations under SLOCC, and that all the n-qubit symmetric Dicke states with l (2 ≤ l ≤ (n − 2)) excitations satisfy Coffman, Kundu and Wootters' generalized monogamy inequality C

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“…For instance, in ref. 19 through a Ramsey fringe-type interference experiment that preserves the quantum state up to a relative phase factor, it was prepared an equal weighted state. On the other hand, in experimental Heisenberg spin chains, the equally weighted superposition of all different localized valence-bond states would correspond to a quantum spin liquid, the so-called resonating valence-bond state [20,21].…”

Section: Introductionmentioning

confidence: 99%

Bounds on the quantity of entanglement in parallel quantum computing of a single ensemble quantum computer

Aoki¹,

Sun²,

Dong

2014

Can. J. Phys.

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Speeding up of the processing of quantum algorithms has been focused on from the point of view of an ensemble quantum computer (EQC) working in a parallel mode. As a consequence of such efforts, additional speed up has been achieved for processing both Shor's and Grover's algorithms. On the other hand, in the literature there is scarce concern about the quantity of entanglement contained in EQC approaches, for this reason in the present work we study such a quantity. As a first result, an upper bound on the quantity of entanglement contained in EQC is imposed. As a main result we prove that equally weighted states are not appropriate for EQC working in parallel mode. In order that our results are not exclusively purely theoretical, we exemplify the situation by discussing the entanglement on an ensemble of n 1 = 3 diamond quantum computers.Résumé : L'accélération de traitement des algorithmes quantiques s'est concentrée sur l'idée d'ordinateur quantique sur les ensembles (EQC) travaillant dans un environnement parallèle. Ces efforts ont mené à une accélération dans le traitement des algorithmes de Shor et de Grover. D'autre part, il y a peu d'intérêt dans la littérature pour le niveau d'intrication dans les approches EQC, et c'est pourquoi nous nous penchons ici sur cette question. Notre premier résultat indique qu'il y a un niveau maximum d'intrication dans une approche EQC. Comme résultat principal, nous prouvons que des états de même poids statistique ne sont pas appropriés pour un EQC travaillant en mode parallèle. Afin que notre résultat ne reste pas un résultat purement théorique, nous prenons en exemple l'intrication d'un ensemble de n 1 = 3 ordinateurs quantiques à diamant. [Traduit par la Rédaction]

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An entanglement measure for n qubits

Cited by 21 publications

References 20 publications

Characterizing scalable measures of quantum resources

Characterizing scalable measures of quantum resources

Stochastic local operations and classical communication properties of the n-qubit symmetric Dicke states

Bounds on the quantity of entanglement in parallel quantum computing of a single ensemble quantum computer

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